Local unitary representations of the braid group and their applications to quantum computing

Local unitary representations of the braid group and their applications to quantum computing

Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.

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Main Authors: Delaney,Colleen, Rowell,Eric C, Wang,Zhenghan
Format: Digital revista
Language:English
Published: Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas 2016
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262016000200006
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spelling oai:scielo:S0034-742620160002000062017-04-17Local unitary representations of the braid group and their applications to quantum computingDelaney,ColleenRowell,Eric CWang,Zhenghan topological quantum computation braid group representations localizations quantum algebra Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.50 n.2 20162016-12-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262016000200006en10.15446/recolma.v50n2.62211
institution SCIELO
collection OJS
country Colombia
countrycode CO
component Revista
access En linea
databasecode rev-scielo-co
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Delaney,Colleen
Rowell,Eric C
Wang,Zhenghan
spellingShingle Delaney,Colleen
Rowell,Eric C
Wang,Zhenghan
Local unitary representations of the braid group and their applications to quantum computing
author_facet Delaney,Colleen
Rowell,Eric C
Wang,Zhenghan
author_sort Delaney,Colleen
title Local unitary representations of the braid group and their applications to quantum computing
title_short Local unitary representations of the braid group and their applications to quantum computing
title_full Local unitary representations of the braid group and their applications to quantum computing
title_fullStr Local unitary representations of the braid group and their applications to quantum computing
title_full_unstemmed Local unitary representations of the braid group and their applications to quantum computing
title_sort local unitary representations of the braid group and their applications to quantum computing
description Abstract We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.
publisher Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
publishDate 2016
url http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262016000200006
work_keys_str_mv AT delaneycolleen localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing
AT rowellericc localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing
AT wangzhenghan localunitaryrepresentationsofthebraidgroupandtheirapplicationstoquantumcomputing
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